Quantum computing is a winsome field that deals with theoretical computational systems (i.e., quantum computers) combining visionary ideas of Computer Science, Physics, and Mathematics. Quantum computing relies upon the quantum phenomena of entanglement and superposition to perform operations. Initially, Feynman [1]} proposed the idea of quantum computing in 1982 after performing a quantum mechanics simulation on a classical computer. In 1994, Shor [2]} designed a quantum algorithm for calculating the factor of a large number n with space complexity \(O(log~n)\)  and time complexity \(O(n^2~log log n)\)  on a quantum computer, and then perform \(O(log~n)\)  post processing time on a classical computer, which could be applied in cracking various cryptosystems, such as RSA algorithm and elliptic curve cryptography. Through the impetus provided by Shor's algorithm, quantum computational complexity is an exhilarating area that transcends the boundaries of quantum physics and theoretical computer science.
